TL;DR: reward feeling is more important than reward number
Reward system should be more about how the current reward system **_feels_** than the actual calculation behind the current reward system. Yes, we will certainly be getting more champions than we did traditionally in the long run by theoretical probability. Suppose we get a malzahar(4800 BE) shard on leveling, camille(6300 BE) shard on next level, Yasuo(6300 BE) shard on next level, and then some bunch of nunu(450 BE) shards on the next level.
In this case, do we get more reward than the traditional system on average? YES! ABSOLUTELY!
So.... do we actually _**feel**_ satisfied with it when bunch of 450 BE shards come out? NO! ABSOLUTELY NOT!!
As shown in the very first paragraph of this wikipedia page, it is an expected human behavior to "make decisions based on the potential value of losses and gains rather than the final outcome, and that people evaluate these losses and gains using certain heuristics" and we players are no exception.
Overwhelming majority of us including myself are not statisticians that think about rewards in terms of numbers. Rather, overwhelming majority of us are simply going to feel a wtf moment whenever those Nunu,Annie,Ryze,etc(450 BE) shards comes out. We players, as human beings, don't rely on calculations to think about [game theory](https://en.wikipedia.org/wiki/Game_theory) to decide what's better for us. Instead, we just make decision by feeling instead.
Unless this issue of human psychology can be dealt with, the new BE system will never feel as rewarding as the traditional IP system despite giving more BE on average, and therefore a failure.